*Gulp*
I'm posting this because it is better to have things out in the open, rather than get blind-sided at some inopportune time. Also,
it ties into the ongoing "worship war" over at Thomisticguy's blog about whether Mormons "worship" Jesus and Catholics "worship" the saints.
Long story, short because of the etymology of the term "worship," which is kind of a catch-all that rusn from honoring our superiors to honoring God, the answer would appear to be "Yes" and "In different degrees."
According to the New Advent Dictionary:
The word worship (Saxon weorthscipe, "honour"; from worth, meaning "value", "dignity", "price", and the termination, ship; Latin cultus) in its most general sense is homage paid to a person or a thing. In this sense we may speak of hero-worship, worship of the emperor, of demons, of the angels, even of relics, and especially of the Cross. This article will deal with Christian worship according to the following definition: homage paid to God, to Jesus Christ, to His saints, to the beings or even to the objects which have a special relation to God.
There are several degrees of this worship:
* if it is addressed directly to God, it is superior, absolute, supreme worship, or worship of adoration, or, according to the consecrated theological term, a worship of latria. This sovereign worship is due to God alone; addressed to a creature it would become idolatry.
* When worship is addressed only indirectly to God, that is, when its object is the veneration of martyrs, of angels, or of saints, it is a subordinate worship dependent on the first, and relative, in so far as it honours the creatures of God for their peculiar relations with Him; it is designated by theologians as the worship of dulia, a term denoting servitude, and implying, when used to signify our worship of distinguished servants of God, that their service to Him is their title to our veneration (cf. Chollet, loc. cit., col. 2407, and Bouquillon, Tractatus de virtute religionis, I, Bruges, 1880, 22 sq.).
* As the Blessed Virgin has a separate and absolutely supereminent rank among the saints, the worship paid to her is called hyperdulia (for the meaning and history of these terms see Suicer, Thesaurus ecclesiasticus, 1728).
In accordance with these principles it will readily be understood that a certain worship may be offered even to inanimate objects, such as the relics of a martyr, the Cross of Christ, the Crown of Thorns, or even the statue or picture of a saint. There is here no confusion or danger of idolatry, for this worship is subordinate or dependent. The relic of the saint is venerated because of the link which unites it with the person who is adored or venerated; while the statue or picture is regarded as having a conventional relation to a person who has a right to our homage — as being a symbol which reminds us of that person.
I'm not entirely sure that I'm happy with the idea of "worshipping" an inanimate object; it just sounds wrong and un-American.
This is interesting:
In virtue of the same principle and of the equality of the Divine Persons in the Trinity, the Holy Ghost also became the object of Christian worship. The formula of baptism was given, as has been seen, in the Name of the Father, and of the Son, and of the Holy Ghost. In the doxology the Holy Spirit also has a place with the Father and the Son. In the Mass the Holy Ghost is invoked at the Epiclesis and invited to prepare the sacrifice. The Montanists, who in the second century preached, and awaited, the coming of the Holy Ghost to take the place of the Son and announce a more perfect Gospel, made Him the object of an exclusive worship, which the Church had to repress. But it nevertheless vindicated the adoration of the Holy Ghost, and in 380 the anathemas pronounced by Pope Damasus, in the Fourth Council of Rome, condemned whosoever should deny that the Holy Ghost must be adored like the Father and the Son by every creature (Denzinger, Enchiridion, n. 80). These anathemas were renewed by Celestine I and Virgilius, and the ecumenical council of 381 in its symbol, which took its place in the liturgy, formulated its faith in the Holy Ghost, "Who together with the Father and the Son is adored and glorified." These expressions indicate the unity of the adoration of the Father, the Son, and the Holy Ghost; that is, that one or the other Person of the Trinity may be adored separately but not to the exclusion of the other two.
It's interesting because it contrasts nicely with the Mormon approach to worshipping the Son,
which was described by Bruce McConkie, on of the LDS Quorum of the 12 Apostles in 1982:
1. We worship the Father and him only and no one else.
We do not worship the Son, and we do not worship the Holy Ghost. I know perfectly well what the scriptures say about worshipping Christ and Jehovah, but they are speaking in an entirely different sense--the sense of standing in awe and being reverentially grateful to him who has redeemed us. Worship in the true and saving sense is reserved for God the first, the Creator.
Our revelations say that the Father "is infinite and eternal," that he created "man, male and female,"
And gave unto them commandments that they should love and serve him, the only living and true God, and that he should be the only being whom they should worship. [D&C 20:17–19]
Jesus said:
True worshippers shall [note that this is mandatory] worship the Father in spirit and in truth; for the Father seeketh such to worship him.
For unto such hath God promised his Spirit. And they who worship him, must worship in spirit and in truth. [JST John 4:25–26]
There is no other way, no other approved system of worship.
And then there is this:
Another peril is that those so involved often begin to pray directly to Christ because of some special friendship they feel has been developed. In this connection a current and unwise book, which advocates gaining a special relationship with Jesus, contains this sentence:
Because the Savior is our mediator, our prayers go through Christ to the Father, and the Father answers our prayers through his Son.
This is plain sectarian nonsense. Our prayers are addressed to the Father, and to him only. They do not go through Christ, or the Blessed Virgin, or St. Genevieve or along the beads of a rosary. We are entitled to "come boldly unto the throne of grace, that we may obtain mercy, and find grace to help in time of need" (Hebrews 4:16).
McConkie's statements are actually a nice working-out of the Arian implications of Mormonism, in contrast to the New Advent's Nicene Christianity. In Nicene Christianity, the Father, Son and Holy Spirit are all God, they are all consubstantial, and so they are worshipped in the same, ultimate way.
In contrast, in Arianism and among the Mormons, the Son is a lesser, created being, and, so, the worship accorded to the Son is less than that accorded to the Father, so much less, in fact, that Mormons can say "we do not worship the Son" in the same way that Catholics say that that "we do not worship saints," although they are both wrong in a sense, and in a sense they are both right.
What is particularly interesting about McConkie's sermon is how he derides both Catholic prayers to the saints and Mormon prayers to Jesus for the same reason, namely they are not directed to God, i.e., to the Suprme Being aka "that than which nothing greater can be thought." So, McConkie accurately observes that prayers are not answered by anything less than the Supreme Being, which according to the LDS' Arian presumptions is not Jesus. Hence, praying to Jesus is essentially - in the LDS scheme of things - wasted effort.
McConkie's conclusion is, thus, that Jesus is a kind of super-saint. It seems that for McConkie, Jesus plays the same role in Mormon theology that Mary plays in Catholic theology, a really super-special, first class created being. Consequently, where Catholics offer "hyperdulia" to Mary, Mormons offer "hyperdulia" to Jesus.
I just find that to be a fascinating comparison.